H. G. Wells is usually credited with having invented the time-travel story in the 1895 classic The Time Machine. In his book Time Travel James Gleick does a good job putting Wells’s invention in context, though I still wonder why such a rich idea lay mostly unexplored until the twentieth century. Clearly we weren’t waiting for science to catch up to our imaginings, because it still hasn’t (and likely never will).
The novel has been freely adapted on film at least twice, by George Pal in 1960 and again, less successfully, in 2002. I would definitely recommend the Pal version, but if you really want a treat you should look for Time After Time, which has Malcolm McDowell playing H. G. Wells zapping forward to 1970s America in a hunt for Jack the Ripper. It’s a movie that’s not very well known these days but it’s very good.